Probably not right away, if I understand your question.
If you are mining cryptocurrency, then the currency you create is taxable income as of the daily value when it is created. Then, if you later sell it for more than the taxable value you first reported, you have a taxable gain based on the gain from the mining price.
If you buy cryptocurrency, your basis is what you paid. When you sell it or use it (convert it to money, goods, or a different cryptocurrency) and the value is more than you paid, you have a taxable capital gain which is the difference between the selling price and purchase price. But you don't pay tax just holding it, only when you convert it to real goods or real money.
If someone gives you cryptocurrency, your basis is the price they originally paid. Then when you sell it or use it, you report a capital gain if you sell for more than the giver's basis. This can be hard to prove, and if you are audited and don't have proof of the giver's basis, the entire value may be taxable. But just holding a gift of cryptocurrency is not a taxable event.
Now, is this a gift, or a premium of some kind? Gifts are not taxable, but you need to know the basis, and if the company gives you free cryptocurrency, then your basis is zero and you pay tax on the entire value when you convert it to something real. Receiving the gift and holding the gift is not reported or taxed, just when you sell it or convert it. And if it is a premium, it reduces the overall basis. For example, suppose you buy 0.1 BTC for $10,000 and receive a 10% bonus of 0.01 free BTC. You now have 0.11 BTC, but your overall basis is still what you paid, $10,000.
I have no idea how you can keep track of all this, stock brokers do it all the time for stock accounts and mutual funds. Hopefully your exchange keeps track and provides you with similar information. If you are even audited and can't prove your basis, the entire amount of any sale or conversion could be taxed.
